A unification of Geraghty type and Ciric type fixed point theorems

Abstract

In the framework of metric spaces, we introduce the concept of Geraghty-Ciric type contractions and show the existence and uniqueness of the fixed point of such mappings. This result improves and unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) and Ciric (Proc. Amer. Math. Soc. 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. In addition, two illustrative examples are provided to indicate the validity of the obtained results.